The following problems require the use of the quotient rule. In the following discussion and solutions the derivative of a function

.

Remember the rule in the following way. Always start with the ``bottom'' function and end with the ``bottom'' function squared. Note that the numerator of the quotient rule is identical to the ordinary product rule except that subtraction replaces addition. In the list of problems which follows, most problems are average and a few are somewhat challenging.

*PROBLEM 1 :*Differentiate .Click HERE to see a detailed solution to problem 1.

*PROBLEM 2 :*Differentiate .Click HERE to see a detailed solution to problem 2.

*PROBLEM 3 :*Differentiate .Click HERE to see a detailed solution to problem 3.

*PROBLEM 4 :*Differentiate .Click HERE to see a detailed solution to problem 4.

*PROBLEM 5 :*Differentiate .Click HERE to see a detailed solution to problem 5.

*PROBLEM 6 :*Differentiate .Click HERE to see a detailed solution to problem 6.

*PROBLEM 7 :*Differentiate .Click HERE to see a detailed solution to problem 7.

*PROBLEM 8 :*Differentiate .Click HERE to see a detailed solution to problem 8.

*PROBLEM 9 :*Consider the function . Evaluate .Click HERE to see a detailed solution to problem 9.

*PROBLEM 10 :*Differentiate .Click HERE to see a detailed solution to problem 10.

*PROBLEM 11 :*Differentiate .Click HERE to see a detailed solution to problem 11.

*PROBLEM 12 :*Differentiate .Click HERE to see a detailed solution to problem 12.

*PROBLEM 13 :*Differentiate .Click HERE to see a detailed solution to problem 13.

*PROBLEM 14 :*Differentiate .Click HERE to see a detailed solution to problem 14.

*PROBLEM 15 :*DifferentiateClick HERE to see a detailed solution to problem 15.

*PROBLEM 16 :*Find an equation of the line tangent to the graph of at*x*=-1 .Click HERE to see a detailed solution to problem 16.

*PROBLEM 17 :*Find an equation of the line tangent to the graph of at .Click HERE to see a detailed solution to problem 17.

*PROBLEM 18 :*Consider the function . Solve*f*'(*x*) = 0 for*x*. Solve*f*''(*x*) = 0 for*x*.Click HERE to see a detailed solution to problem 18.

*PROBLEM 19 :*Find all points (*x*,*y*) on the graph of where tangent lines are perpendicular to the line 8*x*+2*y*= 1 .Click HERE to see a detailed solution to problem 19.

Your comments and suggestions are welcome. Please e-mail any correspondence to Duane Kouba by clicking on the following address :

Tue Jul 29 13:34:53 PDT 1997